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Closed-string amplitude recursions from the Deligne associator
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Inspired by earlier results on recursions for open-string tree-level amplitudes, and by a result of Brown and Dupont relating open- and closed-string tree-level amplitudes via single-valued periods, we identify a recursive relation for closed-string tree-level amplitudes. We achieve this by showing that closed-string analogues of Selberg integrals satisfy the Knizhnik-Zamolodchikov equation for a suitable matrix representation of the free Lie algebra on two generators, and by identifying the limits at z=1 and z=0, which are related by the Deligne associator, with N-point and (N-1)-point closed-string amplitudes, respectively.
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Associators for AdS string amplitude building blocks
Open-string AdS building blocks can be generated by Drinfeld associator recursions and closed-string ones by Deligne associator recursions, yielding all-order zeta-valued expansions.
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